Markup vs Margin
Overview
Markup and margin describe the same price gap against different denominators, and confusing them is a recurring source of retail pricing error. Markup measures profit against cost; margin measures the same profit against selling price. The conversion is margin = markup ÷ (1 + markup), with the inverse markup = margin ÷ (1 − margin). Goods bought at 100 and sold at 150 carry a 50 percent markup but only a 33.3 percent margin, because 50 of profit sits against a 150 sale. The divergence widens sharply as prices rise: a 100 percent markup is a 50 percent margin, and a 300 percent markup a 75 percent margin, so margin can approach but never reach 100 percent. Point-of-sale systems and wholesale price lists frequently quote markup while accounting statements report gross margin, which is why the two figures for one product rarely agree.
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| $Markup$ | Markup rate | decimal or % | Gross profit expressed as a share of cost. |
| $Margin$ | Gross margin | decimal or % | Gross profit expressed as a share of selling price. |
| $C$ | Cost | currency | Cost of goods sold for the unit. |
| $P$ | Price | currency | Selling price of the unit. |
One Profit, Two Denominators
Markup and margin measure the same gross profit against different bases. Markup divides profit by cost; margin divides it by price. The conversion between them is:
$$Margin = \frac{Markup}{1 + Markup} \qquad Markup = \frac{Margin}{1 - Margin}$$
Goods bought at 100 and sold at 150 carry a 50% markup — 50 of profit on 100 of cost — but only a 33.3% margin, because the same 50 sits against a 150 sale.
The Divergence Grows With Price
| Markup | Margin |
|---|---|
| 25% | 20.0% |
| 50% | 33.3% |
| 100% | 50.0% |
| 200% | 66.7% |
| 300% | 75.0% |
Margin approaches but never reaches 100%, since profit cannot exceed the price it is measured against. Markup has no ceiling. A retailer targeting a 40% margin who applies a 40% markup instead prices at 140 rather than the required 166.67 and gives away roughly a sixth of expected gross profit on every unit.
Which Figure Appears Where
Wholesale price lists, point-of-sale systems and buying departments usually work in markup because they start from a known cost. Income statements, investor presentations and industry benchmarks report gross margin because they start from revenue. Both descriptions of one product are correct, which is why they so often appear to disagree.
Derivation & History
Both measures rest on the identity $P = C + \text{profit}$. Writing markup as $m = (P-C)/C$ gives $P = C(1+m)$; writing margin as $g = (P-C)/P$ gives $C = P(1-g)$. Substituting the first into the second yields $C = C(1+m)(1-g)$, so $(1+m)(1-g) = 1$. Solving for $g$ produces $g = m/(1+m)$ and solving for $m$ produces $m = g/(1-g)$. The relation is a Möbius transformation, which is why the mapping is one-to-one and why margin is asymptotic to 1 as markup grows without bound.
Worked Examples
Pricing to a target margin
- Convert the margin to a markup: 0.40 ÷ (1 − 0.40) = 0.6667
- Apply to cost: 120 × (1 + 0.6667) = 200
- Check: (200 − 120) ÷ 200 = 0.40
Result: Price 200 for a 40% margin (a 66.7% markup)
Reading a supplier quote
- Price: 80 × 1.35 = 108
- Margin: 0.35 ÷ 1.35 = 0.2593
Result: 108 selling price, 25.9% gross margin
Edge Cases & Limitations
Margin of 100%: Mathematically requires infinite markup and implies zero cost; the conversion divides by zero.
Selling below cost: Markup and margin both turn negative and the conversion still holds, but a margin below −100% corresponds to selling for less than half of cost.
Which costs are included: Gross margin uses cost of goods sold only. Including freight, duty or overhead produces a different and non-comparable figure, so benchmarks must state the cost basis.
Blended rates: An average markup across a catalogue does not convert to the average margin; each line must be converted before aggregation.
Real-World Applications
Retail buying teams price catalogues from cost-plus markup while finance reports gross margin to investors. Restaurant menu engineering targets a food-cost percentage, the complement of margin. Distribution contracts specify permitted markup bands, and inventory write-down tests compare net realisable value against cost using the same identity.